Orthorhombic URhSi orders ferromagnetically below T-c=9.5 K, with an ordered magnetic moment mu = 0.11 mu(B) per U atom and has a relatively enhanced value of the specific heat c(p)/T = 186 mJ/mol K-2. U-U atomic distances fall in a critical region around the Hill limit so that it is thought to be an itinerant magnet. Our present investigation includes: (i) preparation of high purity crystalline samples further analyzed by single crystal x-ray diffraction and magnetization measurements; (ii) band structure calculations performed with self-consistent full potential linearized Augmented plane wave method within the local density approximation; (iii) optical measurements at room and at low temperature over a large spectral range (2 meV-6 eV). As a result, the details of the crystal structure of URhSi have been refined with respect to previous measurements on powdered samples. The comparison of electronic structure calculations and optical results show: (a) a low mobility of free carriers and a large dielectric screening at the lowest frequencies, connected with excitation off states hybridized with d states at the Fermi level; (b) smooth spectral features due to the huge number and density of states (the main contribution being due to occupied Rh d states). The whole amount of information obtained would suggest the presence of Kondo-like behavior in this compound, independently on the magnetic order.